CBMD

oracq.algorithms.qode.cbmd

Contour-decomposition-based assembly of matrix functions and evolution, explicitly recording the finite series and omitted terms.

class oracq.algorithms.qode.cbmd.ContourPlan(a=1.0, cutoff=2, poles=(2j, -1 + 1j, 1j, 1 + 1j))

Bases: object

QST Eq.12 main series; auxiliary poles and the finite truncation remainder are explicitly retained in the report.

a = 1.0

cutoff = 2

poles = (2j, (-1+1j), 1j, (1+1j))

property nodes

Real nodes of the main series; entry k is k/a with k in -cutoff..cutoff, 2*cutoff+1 in total.

property weights

Complex weights of the main series nodes, in one-to-one correspondence with nodes.

Computed by the residue closed form of QST Eq.12; the denominator contains the (q+i) factor and all auxiliary poles.

property auxiliary_coefficients

Complex coefficients of the auxiliary poles, in one-to-one correspondence with poles.

The corresponding non-Hermitian evolution branches are not generated currently and are only declared in the omitted list of metadata.

metadata()

Export the plan parameters and the omitted-terms declaration as JSON text.

Returns:

Contains a, cutoff, nodes, poles, weights, auxiliary coefficients, the omitted terms, the assumption preconditions, and the source reference.

Return type:

str

oracq.algorithms.qode.cbmd.cbmd_qode(model, time, *, plan=None, hamiltonian_function=<function taylor_hamiltonian>)

Assemble the quantum simulation program for u’=-Au via contour decomposition.

Parameters:

• model – LinearODE input model; parts.hermitian is L, parts.h is H, and initial is the initial state preparation.

• time – Non-negative evolution time.

• plan – ContourPlan contour plan; the default plan is used when omitted.

• hamiltonian_function – Replaceable protocol taking (K, time) and returning a BlockEncoding.

Returns:

Per-node K_k=H+q_k*L branches combined via LCU and applied to the initial state; the success subspace is all-zero signal.

Return type:

StateOracle

Raises:

ValidationError – model or plan has the wrong type, time is invalid, or the input capability contract is not satisfied.

Auxiliary-pole branches and the infinite series tail are not generated and are only declared explicitly in the contour_plan metadata.

oracq.algorithms.qode.cbmd.cbmd_function(a, nodes, residue_weights, hermitian_function)

Generic f(A) assembly point: the Hermitian function protocol stays open and is not silently swapped for matrix inversion.

Parameters:

• a – Block encoding of the target operator A.

• nodes – Residue pole locations, entering the H + q*L combination point by point.

• residue_weights – Complex residue weights in one-to-one correspondence with the poles; the sign convention is the caller’s responsibility.

• hermitian_function – Hermitian function protocol implementation; the input is the block encoding after the pole combination, and it must return a BlockEncoding.

Returns:

The residue-weighted f(A) block encoding, with correctness marked pending.

Return type:

BlockEncoding